Space of modular forms of level 27, weight 9, and Character 27.f

• Label: 27.9.f
• Level: $27$
• Weight: $9$
• Character orbit: 27.f
• Rep. character: $\chi_{27}(2,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $138$
• Newform subspaces: $1$
• Sturm bound: $27$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 27 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(27\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(27, [\chi])\).

	Total	New	Old
Modular forms	150	150	0
Cusp forms	138	138	0
Eisenstein series	12	12	0

Trace form

138 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 447 * q^5 - 774 * q^6 - 6 * q^7 - 9 * q^8 - 12960 * q^9 - 3 * q^10 + 28668 * q^11 + 77421 * q^12 - 6 * q^13 - 120975 * q^14 + 105507 * q^15 - 774 * q^16 - 9 * q^17 - 241317 * q^18 - 3 * q^19 + 137913 * q^20 + 1164372 * q^21 - 185478 * q^22 + 68376 * q^23 - 2624256 * q^24 + 507585 * q^25 + 3500568 * q^27 - 12 * q^28 - 943980 * q^29 - 1533627 * q^30 + 920739 * q^31 - 3005136 * q^32 - 1245285 * q^33 + 660474 * q^34 + 6225408 * q^35 + 4021128 * q^36 - 3 * q^37 - 23716884 * q^38 - 5699685 * q^39 - 975273 * q^40 + 16694382 * q^41 + 1594134 * q^42 + 4412514 * q^43 + 17341119 * q^44 + 12986721 * q^45 - 3 * q^46 - 11341869 * q^47 - 26229183 * q^48 + 11347482 * q^49 - 40948977 * q^50 - 16497396 * q^51 + 14465511 * q^52 + 34106454 * q^54 - 12 * q^55 + 52215771 * q^56 + 26766582 * q^57 - 19078611 * q^58 + 76116738 * q^59 - 24031170 * q^60 + 34059450 * q^61 - 223709616 * q^62 - 149069421 * q^63 + 100663293 * q^64 + 20396037 * q^65 + 83336805 * q^66 - 103603884 * q^67 + 101921427 * q^68 + 38038563 * q^69 + 135373629 * q^70 + 125718795 * q^71 + 183269700 * q^72 - 7632642 * q^73 - 66643887 * q^74 - 167459145 * q^75 - 203790342 * q^76 - 343269159 * q^77 - 344470788 * q^78 - 68767890 * q^79 + 151392924 * q^81 - 12 * q^82 + 383244663 * q^83 + 836800692 * q^84 + 170435619 * q^85 + 71426730 * q^86 - 145695735 * q^87 - 192774918 * q^88 + 135692730 * q^89 - 821329020 * q^90 + 77546796 * q^91 - 1343159175 * q^92 - 414573177 * q^93 - 44451609 * q^94 + 881099997 * q^95 + 1578184830 * q^96 + 31339344 * q^97 + 1293135102 * q^98 + 228876057 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(27, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
27.9.f.a	$27$	$9$	27.f	27.f	$18$	$138$	$23$	$10.999$		None		✓	✓	✓	27.9.f.a	$2$	$0$	\(-6\)	\(-6\)	\(-447\)	\(-6\)		$\mathrm{SU}(2)[C_{18}]$